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 A335939 Bi-unitary weird numbers (A292986) that are not exponentially odd numbers (A268335). 0
 5390, 7400, 11830, 20230, 24010, 25270, 37030, 58870, 67270, 95830, 117670, 129430, 154630, 196630, 243670, 260470, 314230 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Weird numbers (A006037) that are exponentially odd (A268335) are also bi-unitary weird numbers (A292986), since all of their divisors are bi-unitary. LINKS MATHEMATICA fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); biuabQ[n_] := bsigma[n] > 2*n; f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; bweirdQ[n_] := biuabQ[n] && Module[{d = Most @ bdiv[n], x}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bweirdQ[#] &] CROSSREFS Subsequence of A292986. Cf. A006037, A222266, A268335, A335936, A335938. Sequence in context: A058325 A224688 A335936 * A328562 A340109 A190106 Adjacent sequences:  A335936 A335937 A335938 * A335940 A335941 A335942 KEYWORD nonn,more AUTHOR Amiram Eldar, Jun 30 2020 STATUS approved

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Last modified June 27 22:27 EDT 2022. Contains 354899 sequences. (Running on oeis4.)